Real-world networks often have power-law degree distribution, i.e, \(p_k\sim k^{-\alpha }\) , or small-world characteristics [1]}, [2]}. Studies have revealed that the network structures play an important role in dynamical evolutions [3]}. Thus, to mimic real situations, in this section, we examine how our model behaves on multiplex systems composed of two scale-free (SF) networks or two Watts-Strogatz small-world (WS) networks, respectively. All networks have 10000 nodes. The rewiring probability of the two WS networks are both 0.01 and the exponent parameters of the two SF networks are \(\alpha _1=2.7\)  and \(\alpha _2=2.9\) .
